(usually quite large) voltage gain, Av. That’s all we need to
know (at least for this ideal case) about the op-amp.
Let’s analyze an inverting amplifier (Figure 4) just to
see how this works. We’ll add a couple of resistors. One
of these, Rƒ, feeds back the output voltage to the negative
input terminal. The input resistor, Ri, is connected between
that input terminal and the signal. Since the op-amp inputs
do not allow current in, the current through the feedback
resistor, Iƒ, is equal to the current through the input resistor,
Since v+ = 0, then v- = -vo /Av, resulting in:
Also, since Av is typically a very large number (103 < Av
For most practical feedback amplifiers, this equation can
be simplified to:
Getting By with Just
One Power Supply
The Figure 4 schematic shows a ground
reference at the non-inverting input. This circuit (as
with many shown in examples) assumes that the
power supplies to the op-amp are two equal, but
opposite-sign voltages; for example, +12V and -12V.
Such relatively high bipolar voltages were the norm
in earlier times.
In modern microcontroller applications, the
microcontroller and other digital functions are
typically powered from + 3.3V or a similar single
low voltage. A dual supply — particularly like the
traditional ±12V setup — is inconvenient; both because of
the higher voltages required and because a negative voltage
is needed. Fortunately, many modern op-amps are capable
of operating from voltages in the 3V to 5V range.
To do this, we use the + 3.3V (or whatever voltage level
we are using) as the positive op-amp supply voltage and use
ground as the negative supply voltage. We create a voltage
that’s about half of the positive supply voltage and reference
all voltages to that. How does that work?
Let’s take another look at the inverting amplifier, but
this time using a single supply voltage (Figure 5).
The input voltage, vi’ has the apostrophe added to
indicate that it has a 1.65V DC pedestal. That is:
We’ll also use vo’ to indicate that it could have a DC level
added, although we haven’t determined yet what that DC
level is. Again, using the fact that Ii = Iƒ the resulting voltage
Figure 5. Single supply
Most microcontroller programs — whether by hobbyists or
professionals — are written in a high-level language such as C or Python
(Arduino users often use Sketch; a
variant of C). The MSP430 is also readily
programmable in these high-level
languages (the Sketch equivalent for
the MSP430 is called Energia). I prefer
Assembly language for sensor projects,
mainly because of the greater peripheral
control that it gives me and the greater
flexibility it gives me in debugging
Figure 4. Inverting amplifier.
10 SERVO 09/10.2018